A frictionless positioning device using cone-shaped active magnetic bearings(AMBs) is developed, which is driven by a brushless DC motor equipped with resolver. The cone-shaped AMB feature that the structure is simple and yet the five d.o.f. rotor motion is controlled by four magnet pairs. A linearized dynamic model, which accounts for the relationship between input voltage and output current in the cone-shaped magnet, is developed and the azimuth motion of the frictionless positioning device is modeled as the second order system. The feedback controller is designed by using linear quadratic regulator with integral action optimal control law so that the cone-shaped AMB system is stabilized and the frictionless positioning device gets the zero steady state. It is observed that the linearized dynamic model is adequate and the frictionless positioning device can achieve the tracking accuracy within the sensor resolution.